Divide Rs. 169 in the ratio 2:5:6. The rupees in the respective ratios are given by

Options

A. 26,66 & 77
B. 26, 65 & 78
C. 25, 67 & 78
D. 26,70 & 73

Answer

To solve the problem of dividing Rs. 169 in the ratio 2:5:6, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Ratio**: The ratio 2:5:6 means that for every 2 parts, there are 5 parts and 6 parts respectively. We can denote these parts as 2X, 5X, and 6X.

2. **Set Up the Equation**: According to the problem, the total amount (Rs. 169) is equal to the sum of the parts:
\[ 2X + 5X + 6X = 169 \]

3. **Combine Like Terms**: Combine the terms on the left side of the equation:
\[ (2 + 5 + 6)X = 169 \]
This simplifies to:
\[ 13X = 169 \]

4. **Solve for X**: To find the value of X, divide both sides of the equation by 13:
\[ X = \frac{169}{13} = 13 \]

5. **Calculate Each Share**:
- For the first part (2X):
\[ 2X = 2 \times 13 = 26 \]
- For the second part (5X):
\[ 5X = 5 \times 13 = 65 \]
- For the third part (6X):
\[ 6X = 6 \times 13 = 78 \]

6. **Final Shares**: The amounts in the respective ratios are:
- First share: Rs. 26
- Second share: Rs. 65
- Third share: Rs. 78

### Summary of the Solution:
The amounts in the respective ratios of 2:5:6 are Rs. 26, Rs. 65, and Rs. 78.